1. N2 – Dimensional Analysis
Also known as “Unit Conversion”

2. Remember - Canceling Units
One on top cancels with one on the bottom y
xy =
3 cm2
15 cm3 = x
5 cm

3. Conversion Factors
A relationship between how many of one thing equals how many of another thing
12in = 1ft hrs = 1,440min m = 1km
You can rewrite as fractions:
12in = hr = km = ft ,440min m

4. Conversion Factors You can flip conversion factors too
12in = 1ft hrs = 1,440min
Just depends on what you are doing
12in = ft = hr = ,440min = ft in 1,440min hr

5. Using Conversion Factors
If you multiply by a conversion factor, you are just multiplying by 1…your answer LOOKS DIFFERENT because of the unit but is the same SIZE MEASURMENT. (12in/1ft or 1ft/12in)
85 𝑖𝑛𝑐ℎ𝑒𝑠 𝑥 1𝑓𝑡 12 𝑖𝑛 =7.1 𝑓𝑡

6. Using Conversion Factors
You can use multiple conversion factors – “a frog hopping across a pond on lily pads”
Convert 3.6mi into cm. (1cm=0.3937in, 12in=1ft, 1mi=5,280ft)
3.6𝑚𝑖 𝑥 5280𝑓𝑡 1 𝑚𝑖 𝑥 12𝑖𝑛 1 𝑓𝑡 𝑥 1𝑐𝑚 𝑖𝑛 =5.8𝑥105𝑐𝑚

7. 15𝑦𝑟𝑠 𝑥 365𝑑𝑎𝑦𝑠 1 𝑦𝑟 𝑥 24ℎ𝑟𝑠 1 𝑑𝑎𝑦 𝑥 60𝑚𝑖𝑛 1ℎ𝑟 =7.9𝑥106𝑚𝑖𝑛
You try one…
Convert 15years into minutes
15𝑦𝑟𝑠 𝑥 365𝑑𝑎𝑦𝑠 1 𝑦𝑟 𝑥 24ℎ𝑟𝑠 1 𝑑𝑎𝑦 𝑥 60𝑚𝑖𝑛 1ℎ𝑟 =7.9𝑥106𝑚𝑖𝑛

8. Dimensional Analysis with “Derived/Double Units”
Some units are combinations of two or more other units. Like miles per hour (mi/hr). Fix the top unit, then go back and fix the bottom unit
Convert 20mi/hr into in/sec.
20mi
5280ft
12in
1hr
1min
1mi
1ft
60min
60sec
= 𝑖𝑛 𝑠𝑒𝑐

9. = 68.4 𝑓𝑡 𝑚𝑖𝑛 You try one… 30km 1000m 39.37in 1foot 1day 1hr 1km 1m
Convert 30km/day into ft/min (1m=39.37in)
30km
1000m
39.37in
1foot
1day
1hr
1km 1m
12in
24hr
60min
= 𝑓𝑡 𝑚𝑖𝑛